Three-dimensional orbifolds by 2-groups

TL;DR

This paper extends the theory of three-dimensional orbifolds by 2-groups, providing a generalized decomposition framework, computational methods, and numerous examples confirming the conjecture's validity.

Contribution

It introduces a broader class of 2-group orbifolds, generalizes the decomposition conjecture, and demonstrates its validity through detailed computations.

Findings

Decomposition holds for new classes of 2-group orbifolds

Explicit computations confirm the generalized decomposition conjecture

Framework applicable to physical models involving orbifolds

Abstract

In this paper we generalize previous work on decomposition in three-dimensional orbifolds by 2-groups realized as analogues of central extensions, to orbifolds by more general 2-groups. We describe the computation of such orbifolds in physics, state a version of the decomposition conjecture, and then compute in numerous examples, checking that decomposition works as advertised.